Ode - Convert into System of Differential Equations

Convert {see attachment} into a system of differential equations and classify the resulting system

Ode - Solve the System of Differential Equations

Subject to the conditions x(0) = 0 and y(0) - 1, completely solve the following system of differential equations: {see attachment}

Ode: Equilibrium Points; Linearize

Consider the attached system of differential equations. a. Find the equilibrium points associated with this system b. Linearize the system about each of the equlibrium points you find in part a.

Ode

Please solve the attached problem (subject to the given initial conditions)

Ode (General Solution; Phase Portrait

a. Find the general solution to the attached system of differential equations b. Draw the phase portrait for this system and describe in words what happens to the solution for all initial conditions: {see attachment}